Chapter 12.5, Problem 34PPSE

Solution

To find : The needed transformation to do first to describe the motion.

  

Instead of using eight rotation matrices, using the rotation matrix for $360°$ can be used.

Given information :

In upcoming cartoon, the hero is a gymnast and four frames of movie show below movements.

  

Explanation :

The given figure has the vertices with coordinates $A\left(0,-1\right),B\left(-2,-3\right),C\left(0,-7\right),D\left(2,-3\right)$ .

The preimage matrix is $\left[\begin{array}{cccc}0& -2& 0& 2\\ -1& -3& -7& -3\end{array}\right]$ .

The rotation matrix required from frame 1 to frame 2 is $\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$ .

The rotation matrix required from frame 2 to frame 3 is $\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$ .

The rotation matrix required from frame 3 to frame 4 is $\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$ .

The rotation matrix required from frame 4 to frame 5 is $\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$ .

The rotation matrix required from frame 5 to frame 6 is $\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$ .

The rotation matrix required from frame 6 to frame 7 is $\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$ .

The rotation matrix required from frame 7 to frame 8 is $\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$ .

Thus, instead of using eight rotation matrices, using the rotation matrix for $360°$ can be used.